Figure 5.

Illustration of the advantage and robustness of the bootstrap procedure over the one-sample
t-test confidence interval. From A to D, histograms of the grey matter values across subjects are plotted for
the maximum of the average image, the standard deviation image, the kurtosis image
and the skewness image. As illustrated (data distribution in blue), data did not conform
well (bias) to the normal distribution. This resulted in an over-estimation of the
CI size using a one sample t-test (red dotted lines on the CI evolution graphics).
By contrast, bootstrapped CI sizes were narrower (blue lines on the CI evolution graphics).
This is illustrated over the whole brain on brain renders E and F. Overall, bootstrapped
and t-test CI were similarly distributed (E) but bootstrapped CI were in general narrower
(warm colours in F). The average one-sample t-test CI size was 0.0486 ± 0.0096 (min
0.0198, max 0.096, median 0.0474) vs. 0.0461 ± 0.0091 (min 0.0188, max 0.0895, median
0.045) for the 5000 resamples bootstrap CIs. This difference was statistically significant
(t(251572) = 65.25 p < .00001), illustrating the advantage of the bootstrap approach,
even if the majority of brain voxels have a close to Normal distributions (G – Lilliefors
test > .05 – arrows and circles indicates the few 'non-normal' voxels). Graphics titled
'CI size' illustrate the evolution of the bootstrapped CI size with the number of
resamples. The vertical dotted line mark the 3000th resample, from which CI size tend to be stable. On the right hand side, graphics titled
'Means' show the distribution of the data means after 5000 resample (to compare with
the original 'data distribution') from which the last bootstrapped CIs were obtained.